Lets imagine, for a moment, we were trying to make AC scale like Attack does. Attack scales with proficiency, and if you're starting with a 16 in your attack stat, an additional +2. So you're gaining +6 over your career.
Armor scales at +2 currently; heavy armor wearers upgrade from chainmail to splint to plate. Light armor wearers, at least Rogues and the like, are likely starting with 16 Dex and studded leather (at least rather quickly, since it costs less than chainshirt, scalemail, or chainmail). They're going to get +2 to their Dex mod from ASIs.
So, AC currently, doesn't scale much. Now, there are more items that grant AC bonuses than there are items that grant attack bonuses, so maybe that was the intent. But, the Monk's AC can scale by +5, if they start with Dex 16 and Wis 14 (which gives them equivalent AC as Studded Leather and Dex 16) from their ASIs, and they get access to many of the same AC boosting items (just no shields and armor).
Having the AC calculation be changed to 8+Prof+Dex, and then adjusting the armors, could work. It would be an AC boost, though, so you might want to adjust some of the magic AC boosting items (like ring of protection, magic shields, and the like).
I'd be wary of having medium and heavy armor wearers have a lower defense score (which is what I'd call it if you were taking away armor granting an AC bonus, and switching it for armor HP or damage reduction).